Hausdorff Center for Mathematics Courses

On Serre's Thin Set Conjecture

Explore Serre's conjecture on counting rational points in thin sets, focusing on type II sets via determinant methods and recent collaborative research advances.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Hrushovski Construction in Ordered Fields

Explore advanced model theory through Hrushovski construction applied to ordered fields, examining strongly minimal theories and field expansions with multiplicative subgroups.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Hilbert Tenth Problem for Finitely Generated Rings

Explore advanced techniques for constructing elliptic curves with prescribed rank to resolve Hilbert's tenth problem for finitely generated rings using diophantine methods.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Classifying First Order Theories by Borel Reducibility - Status Report

Explore Borel complexity of countable models in first-order theories, examining dividing lines, canonical Scott sentences, groundedness, flat structures, and nested sequences with examples.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Multi-Topological Fields, Approximations and NTP2

Explore unified properties of pseudo-algebraically closed fields through model-theoretic classification and approximation results in topological field theory.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Recursively Saturated Real Closed Fields and Models of Peano Arithmetic

Explore the connection between real closed fields with integer parts and Peano arithmetic models, featuring valuation theory and recursive saturation characterizations.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Expansions of Real-Closed Fields - Expansions of Presburger Arithmetic

Explore tame expansions of real-closed fields and Presburger arithmetic, examining their connections through additive reducts of integer parts in this mathematical research presentation.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Beautiful Pairs of Algebraically Closed Valued Fields and Non-Standard Frobenius

Explore beautiful pairs in algebraically closed valued fields and their applications to definability questions, featuring Ax-Kochen-Ershov reductions and non-standard Frobenius.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

Isomorphism Problems as Equivalence Relations

Explore how isomorphism problems in algebra connect to computability theory, examining classification of algebraic structures and their computational complexities.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Scott Filtrations and Vaught Ordinals

Explore Scott filtrations connecting Scott rank and back-and-forth relations in computable structure theory, examining complexity of isomorphism relations up to Vaught ordinals.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Alignments of Definable Groups and Explicit Bounds in General Elekes-Szabó

Explore advanced model theory techniques for analyzing algebraic variety intersections with finite grids, focusing on o-minimal cases and explicit bounds in Elekes-Szabó theorems.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Cohomological Obstructions to Rational Points

Explore cohomological obstructions proving varieties over number fields lack rational points, covering Brauer-Manin and descent obstructions in this advanced mathematics lecture.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Models of Peano Arithmetic and Chain Rings

Explore the intricate connections between residue rings of Peano Arithmetic models and chain rings in this advanced mathematical presentation.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

The Borel Monadic Theory of Order is Decidable

Discover the decidability of Borel monadic theory of order, exploring connections between automata theory, set theory, and determinacy hypotheses in mathematical logic.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Cohesive Powers of Algebraic Number Fields

Explore computability-theoretic ultrapower constructions using cohesive sets to analyze algebraic properties of number fields and their first-order theories.

• YouTube
• 40 minutes
• Self-Paced
• Free Video